Gravitational Force Calculation

Calculating the Gravitational Force

A small planet having a radius of 1000 km exerts a gravitational force of 100 N on an object that is 500 km above its surface. If this object is moved 500 km farther from the planet, the gravitational force on it will be closest to A) 71 N. B) 25 N. C) 56 N. D) 50 N. E) 75 N.

Option C is the correct answer.

Explanation:

Gravitational force is given by: \[ F = \frac{GMm}{r^2} \]

Where:

  • G = 6.674×10⁻¹¹ m³⋅kg⁻¹⋅s⁻²
  • M = Mass of object 1
  • m = Mass of object 2
  • r = Distance between objects

Here only the variable is the r value.

In case 1: \[ 100 = \frac{GMm}{(1000+500)^2} \] \[ GMm = 100 \times 1500^2 \]

In case 2: \[ F = \frac{GMm}{(1000+500+500)^2} \] \[ F = \frac{GMm}{2000^2} \] \[ F = \frac{100 \times 1500^2}{2000^2} \] \[ F = 56.25 \, \text{N} \]

Therefore, the gravitational force on the object, when moved 500 km farther from the planet, will be closest to 56 N, which is option C.

If a small planet having a radius of 1000 km exerts a gravitational force of 100 N on an object that is 500 km above its surface, what will be the gravitational force on the object if it is moved 500 km farther from the planet?

The gravitational force on the object, when moved 500 km farther from the planet, will be closest to 56 N.

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